A systematic approach to noise reduction in chaotic hydrological time series

Sivakumar, Bellie; Phoon, Kok‐Kwang; Liong, Shie‐Yui; Liaw, C.Y.

doi:10.1016/s0022-1694(99)00051-7

Cited by 75 publications

(41 citation statements)

References 35 publications

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“…Also, recent studies (e.g. Sivakumar et al, 1999b;Sivakumar, 2000) reveal that, while small levels of noise influence significantly the accuracy of prediction estimates, the correlation dimension estimates are not influenced significantly (i.e. overestimated) even when noise levels are high.…”

Section: Analyses Results and Discussionmentioning

confidence: 97%

“…Havstad and Ehlers, 1989;Schreiber and Kantz, 1996;Sivakumar et al, 1999b). It is important to note, however, that there could also be other problems, as serious as or even more serious than the above, that might not have received the necessary attention because of their association with a particular field.…”

Section: Analyses Results and Discussionmentioning

confidence: 98%

“…Sivakumar et al, 1999b;Sivakumar, 2000). The (highest resolution) daily rainfall series is contaminated by both measurement noise (due to the influence of wind, wetting, evaporation, gauge exposure, instrumentation and human error in reading the data) and dynamical noise.…”

Section: Analyses Results and Discussionmentioning

confidence: 99%

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Rainfall dynamics at different temporal scales: A chaotic perspective

Sivakumar

2001

Hydrol. Earth Syst. Sci.

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This study of the behaviour of rainfall dynamics at different temporal scales identifies the type of approach most suitable for transformation of rainfall data from one scale to another. Rainfall data of four different temporal scales, i.e. daily, 2-day, 4-day and 8-day, observed over a period of about 25 years at the Leaf River basin, Mississippi, USA, are analysed. The correlation dimension method is employed to identify the behaviour of rainfall dynamics. The finite correlation dimensions obtained for the four rainfall series (4.82, 5.26, 6.42 and 8.87, respectively) indicate the possible existence of chaotic behaviour in the rainfall observed at the four scales. A possible implication of this might be that the rainfall processes at these scales are related through a chaotic (scale-invariant) behaviour. However, a comparison of the correlation dimension and coefficient of variation of each of the time series reveals an inverse relationship between the two (higher dimension for lower coefficient of variation and vice versa). The presence of a large number of zeros in the higher resolution time series (that could result in an underestimation of the dimension) and the possible presence of a higher level of noise in the lower resolution time series (that could result in an overestimation of the dimension) might account for such results. In view of these problems, it is concluded that the results must be verified using other chaos identification methods and the existence of chaos must be substantiated with additional evidence.

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Section: Analyses Results and Discussionmentioning

confidence: 97%

Section: Analyses Results and Discussionmentioning

confidence: 98%

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Rainfall dynamics at different temporal scales: A chaotic perspective

Sivakumar

2001

Hydrol. Earth Syst. Sci.

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“…Therefore, it is often helpful, and necessary, to use as many ways as possible to be more confident of the scaling region identification and correlation exponent estimation. Further details on the effects of noise on the correlation dimension estimate, in particular reference to hydrologic data (rainfall), are presented in, for example, Sivakumar et al (1999b), and the interested reader is directed to such. In view of the above, we use not only the local slope versus Log r for identification and estimation (shown in Fig.…”

Section: Analysis and Resultsmentioning

confidence: 99%

Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework

Sivakumar

Singh

2012

Hydrol. Earth Syst. Sci.

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131

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Abstract. The absence of a generic modeling framework in hydrology has long been recognized. With our current practice of developing more and more complex models for specific individual situations, there is an increasing emphasis and urgency on this issue. There have been some attempts to provide guidelines for a catchment classification framework, but research in this area is still in a state of infancy. To move forward on this classification framework, identification of an appropriate basis and development of a suitable methodology for its representation are vital. The present study argues that hydrologic system complexity is an appropriate basis for this classification framework and nonlinear dynamic concepts constitute a suitable methodology. The study employs a popular nonlinear dynamic method for identification of the level of complexity of streamflow and for its classification. The correlation dimension method, which has its base on data reconstruction and nearest neighbor concepts, is applied to monthly streamflow time series from a large network of 117 gaging stations across 11 states in the western United States (US). The dimensionality of the time series forms the basis for identification of system complexity and, accordingly, streamflows are classified into four major categories: low-dimensional, medium-dimensional, highdimensional, and unidentifiable. The dimension estimates show some "homogeneity" in flow complexity within certain regions of the western US, but there are also strong exceptions.

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“…The real time series is always expected to be contaminated by some level of noise. It is, however, shown by Sivakumar et al (1999c) that the presence of noise significantly affects the prediction accuracy and the correlation dimension estimates are not influenced even for high noise levels. The authors argue that the correlation dimension estimation could be attempted for preliminary investigation of character of chaos in the hydrological data.…”

Section: Time Series Analysis Methodologymentioning

confidence: 99%

Deep bore well water level fluctuations in the Koyna region, India: the presence of a low order dynamical system in a seismically active environment

Ramana

Chelani

Chadha

et al. 2009

Nonlin. Processes Geophys.

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Abstract. Water level fluctuations in deep bore wells in the vicinity of seismically active Koyna region in western India provides an opportunity to understand the causative mechanism underlying reservoir-triggered earthquakes. As the crustal porous rocks behave nonlinearly, their characteristics can be obtained by analysing water level fluctuations, which reflect an integrated response of the medium. A Fractal dimension is one such measure of nonlinear characteristics of porous rock as observed in water level data from the Koyna region. It is inferred in our study that a low nonlinear dynamical system with three variables can predict the water level fluctuations in bore wells.

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A systematic approach to noise reduction in chaotic hydrological time series

Cited by 75 publications

References 35 publications

Rainfall dynamics at different temporal scales: A chaotic perspective

Rainfall dynamics at different temporal scales: A chaotic perspective

Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework

Deep bore well water level fluctuations in the Koyna region, India: the presence of a low order dynamical system in a seismically active environment

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